Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems Hamid Jafarkhani Center for Pervasive Communications and Computing University of California, Irvine http://newport.eecs.uci.edu/∼hamidj/ Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless B 1 / 64
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Distributed Beamforming and CooperativeCommunications for Next Generation Wireless
Broadband Systems
Hamid Jafarkhani
Center for Pervasive Communications and ComputingUniversity of California, Irvine
http://newport.eecs.uci.edu/∼hamidj/
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems1 / 64
Outline
Trends in wireless communication technologies
Cooperative Communications
Beamforming
Distributed (network) beamforming
Distributed beamformnig with quantized feedback
Distributed beamforming in relay-interference networks withquantized feedback
Conclusions
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems2 / 64
Characteristics of D2D Networks
Very large number of nodes (Trillion ?)I Sensor networks are used more oftenI Body area networks are gaining more attention
Self organized and autonomously operated
Operating through different domains (wireless and wired)seamlessly
Low latency
Low power
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems3 / 64
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems8 / 64
MIMO
Multiple antennas can be utilized toI Increase the throughput (Higher capacity)I Improve the reliability (Diversity)
......
Transmitter Receiver
......
Transmitter Receiver
Feedback
Closed loop system
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems9 / 64
Coordinated Multi-Point
Coherently coordinating the transmission and reception amongmultiple base stations
1
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems10 / 64
ICIC (Heterogeneous Networks)
Offloading: traffic from dual-mode devices over Wi-Fi andsmall-cell networks
45% of the total mobile data traffic from all mobile-connecteddevices is offloaded
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems11 / 64
Sources of Interference in HetNet
Large number of created cell boundaries
The adhoc nature of femto cell deployment
Power difference between nodes
Strong local signal of a femto cell can become interference for alocal user who is not subscribed to the femto cell
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems12 / 64
Need for a paradigm shift
Current wireless networks include many users and many datatransmitted simultaneously, but we allocate independentresources through routing, scheduling, · · · to send A’s messageto B without interference
What if we literally allow simultaneous transmission?
Point-to-Point =⇒ Many-to-Many
Competition =⇒ Cooperation
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems13 / 64
Many to many
Transmitter-1
Transmitter-2
Receiver-1
Receiver-2
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems14 / 64
Many to many with cooperation
......
...
...
...
...
...
+
+
Transm
itter 1
Transm
itter K
Receiv
er1
Receiv
erL
Relay1
Relay2
RelayR−1
RelayR
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems15 / 64
MIMO advantages
......
Transmitter Receiver
Multiplexing gain
Diversity
Array gain
Interference cancellation
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems16 / 64
Diversity and array gain
0 2 4 6 8 10 12 14 16 18 2010
−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
Bit
Err
or R
ate
(BE
R)
Signal−to−Noise Ratio (SNR), (dB)
Performance of a wireless communication system
Diversity gain = 2
Diversity gain = 4
Diversity gain = 4,and more array gain
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems17 / 64
Relay networks
......
...
Transm
itter R
eceiver
Relay1
Relay2
RelayR−1
RelayR
1
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems18 / 64
Cooperative strategies
Amplify and forward
Decode and forward
Coded cooperation
Compress/estimate and forward
Distributed space-time coding
· · ·
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems19 / 64
Amplify and forward
A simple and easy to implement protocol:I The relay amplifies its received signal t by a factor a.I a may depend on channel states, etc.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems20 / 64
Decode and forward
In general s 6= s (decoding errors).I Good performance especially when the source-to-relay channel is good.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems21 / 64
Distributed space-time coding
One can generate a space-time code using multiple distributed relays.I No need for CSI at relays, full spatial diversity, usually with simple
decoding.
......
... +
Transm
itter R
eceiver
s y
Relay1
Relay2
RelayR−1
RelayR
r1 t1
r2 t2
rR−1 tR−1
rR tR
f1
f2
fR−1
fR
g1
g2
gR−1
gR
1
s =[s1 · · · sT
]Tri = fis + ν i yi =
∑Ri=1 giti + w
ti = Ai ri + Bi ri
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems22 / 64
Properties ofdistributed space-time codes
Full diversity
Simple decoding
Simple relaying (linear codewords)
Scale-free: If some of the relays do not exist, the codestill works and provides the highest possible diversity.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems23 / 64
Distributed beamforming
What if we know all the channel information at therelays as well?
Separate short-term power constraints on relays.
Adaptive Relay Power Control
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems24 / 64
Distributed beamforming
......
... +
Transm
itter R
eceiver
s y
Relay1
Relay2
RelayR−1
RelayR
r1 t1
r2 t2
rR−1 tR−1
rR tR
f1
f2
fR−1
fR
g1
g2
gR−1
gR
1
ti = xi ri = αiejθi ri .
Power constraint on each relay Pi .
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems25 / 64
MIMO beamforming
xi = αiejθi with αi = |hi |
‖h‖ , θi = − arg(hi).
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems26 / 64
MIMO beamforming withperfect feedback
Scalar coding and 1-dimensional beamforming is optimal.
Beamforming provides the maximum array gain and full diversity.
Tx
Rx
BeamTx
Rx
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems27 / 64
MIMO channel with feedback
......
Transmitter Receiver
Feedback
Closed loop system
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems28 / 64
Importance of limited feedback
About 30% of the traffic is feedback:I Physical locationI Channel state information (CSI)I RTS/CTS, ACK and other signalingI · · ·
Role of feedbackI BeamformingI PrecodingI Power/rate controlI Collision controlI Routing and schedulingI Resource management/allocationI · · ·
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems29 / 64
Channel feedback quality
If the feedback quality drops too low, thebeamforming scheme should gradually fall back to thenon-beamformed scheme.
Perfect Channel Feedback =⇒ Beamforming
No Channel Feedback =⇒ Space-Time Coding
What shall we do in between?
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems30 / 64
High quality feedback links
Diversity Gain Array Gain
Space-time Coding M 1
Perfect beamforming M M
Quantized beamforming M M − (M − 1)2−r
M−1
To achieve the full CSIT, perfect beamforming results, do we reallyneed r =∞ bits of feedback?
Is there a similar analysis for distributed beamforming, i.e., for relaynetworks?
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems31 / 64
Block diagram of a quantizedbeamforming system
Transmitter
Receiver
Inputbits
Baseband singledata stream
Use the codewordto transmit
Codebook
ChannelEstimation
FeedbackChannel
Select thebest codeword
Codebook
DecoderDecoded
bits
1
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems32 / 64
Outage probability as an example
h
Transmitter Receiver
The M-antenna transmitter wishes to communicate with data rate ρand has a power constraint P. The channel state is h ∈ CM .
The transmitter sends sx?√P.
I s ∈ C is a unit-energy Gaussian symbol.I x ∈ CM is a unit-norm beamforming vector.
Maximum reliable communication rate log2(1 + |〈x,h〉|2P).1 P-normalized SNR |〈x,h〉|2 < α , 2ρ−1
P : Outage.2 |〈x,h〉|2 ≥ α: No outage.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems33 / 64
Variable-length feedback
Quantizer q := {xn, En, bn}I .
h
Find n with h ∈ En
Transmitter
Uses xn = q(h)
Receiver
Feed back bn
Channel: h ∼ CN(0, IM).
Quantized beamforming vector: q(h) ∈ CM with ‖q(h)‖ = 1.
{bn}I ⊂ {ε, 0, 1, 00, 01, . . .}.We are in outage if |〈q(h),h〉|2 < α.
Minimize the outage prob. P(|〈q(h),h〉|2 < α) s.t. R(q) ≤ r .
The best outage probability is out? = P(‖h‖2 < α).
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems34 / 64
Fixed-length designs
A fixed-length quantizer that is optimal forcodebook B:
qB(h) = arg maxx∈B|〈x,h〉|2.
How to design a good codebook:I Distribute the reproduction vectors
“uniformly” on the unit-norm complexhypersphere: Grassmannian codebooks,etc.
outf (r) ∼ out? + CαM
eα 2−r
M−1 [Mukkavilli et al.,
2003]
x1
x2
x3
x4
‖h‖ = 1
‖h‖ = ∞
1
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems35 / 64
Variable-length designs - Take 1
Try: Fixed-length codecells +variable-length code. Does not work.
Then, is outv (r) ∼ outf (r) > out??
No, we can do much better.outv (r0) = out? at finite r0.
x1
x2
x3
x4
‖h‖ = 1
‖h‖ = ∞
1
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems36 / 64
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems39 / 64
Results
Theorem
The minimum (Full-CSIT) outage probability is achievable with rater0 , e−α[α + C (α2 + αt)].
Recall α = 2ρ−1P .
r0 → 0 as r0 ∈ α + o(α) for α→ 0 (High transmission power).
r0 → 0 for α→∞ (Low transmission power).
Achieving the performance of the full-CSIT system with a finitefeedback rate is possible!
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems40 / 64
Example: 2× 1 system
R(q⋆F)
OUT(open)
OUT(q⋆F)
OUT(Full)
P (dB)
Outage
probab
ilityor
Feedbackrate
10
1
10−1
10−2
10−3
10−4
10−5
10−6
−10 −5 0 5 10 15 20 25 30
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems41 / 64
Distributed beamforming withperfect feedback
......
... +
Transm
itter R
eceiver
s y
Relay1
Relay2
RelayR−1
RelayR
r1 t1
r2 t2
rR−1 tR−1
rR tR
f1
f2
fR−1
fR
g1
g2
gR−1
gR
1
ti = xi ri = αiejθi ri .
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems42 / 64
Distributed beamformingproblem formulation
Optimize the received SNR:
maxx
|〈f,Ax〉|2P0
1 + ‖Ax‖2 = maxy
P0|〈c, y〉|21 + ‖y‖2 ,
where f =[f1 · · · fR
]H, and A = diag
{g1√P1√
1+|f1|2P0· · · gR
√PR√
1+|fR |2P0
}.
Total power constraint:‖x‖2 ≤ 1.
1
Individual power constraint:‖x‖∞ ≤ 1 (|xi | ≤ 1, ∀i).
1
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems43 / 64
Comparing MIMO &distributed beamforming
Differences:
IAntennas can share power in MIMO (total powerconstraint), ‖x‖2 ≤ 1.
1
I Antennas know the transmitted signals perfectly in MIMO.
Consequences:
IIndividual (separate) power constraints, ‖x‖∞ ≤ 1.This results in a non-convex optimazation problem.
1
I Distributed solutions.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems44 / 64
Distributed solution
An analytical closed-form solution exists despite the non-convex nature
of the optimization problem.
Properties of the optimal solution:I The optimal xi is not binary.I At least one relay uses its full power.I The optimal xi depends on all the channels, not just the ith relay’s
channels.I The optimal beamforming coefficient can be calculated using
1 A global parameter (fed back by the receiver), and2 A local parameter (calculated using the relay’s own channels).
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems45 / 64
Simulation results:2 Relays (BPSK)
10 12 14 16 18 20 22 24
10−4
10−3
10−2
10−1
Power (dB)
Blo
ck e
rror
rat
e
Alamouti DSTCNetwork beamformingBest relay selectionAF without power control
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems46 / 64
Simulation results:3 Relays (BPSK)
6 8 10 12 14 16 1810
−4
10−3
10−2
10−1
Power (dB)
Blo
ck e
rror
rat
e
AF without power controlNetwork beamformingBest relay selection
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems47 / 64
Relay networks withquantized feedback
......
... +
Transm
itter R
eceiver
s y
Relay1
Relay2
RelayR−1
RelayR
t1 u1
t2 u2
tR−1 uR−1
tR uR
f1
f2
fR−1
fR
g1
g2
gR−1
gR
B feedback bits
1
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems48 / 64
Relay networks withquantized feedback
......
... +
Transm
itter R
eceiver
s y
Relay1
Relay2
RelayR−1
RelayR
t1 u1
t2 u2
tR−1 uR−1
tR uR
f1
f2
fR−1
fR
g1
g2
gR−1
gR
B feedback bits
1
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems49 / 64
Distributed beamforming withlimited feedback
Each relay has B bits of partial CSI provided by thereceiver.
The feedback channel is error-free and delay-free.
The information each relay receives from the feedbackis the same.
Common codebook: C = {x1, . . . , xM}, containsM = 2B beamforming vectors.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems50 / 64
Main results
Maximal diversity with the relay selection scheme
The relay selection scheme achieves the full diversity order R forB = dlog2 Re.In general, the diversity order min(2B ,R) is achievable with quantizedfeedback.
SNR/Capacity loss with quantized feedback
Both the ergodic capacity loss and the SNR loss with quantizedfeedback decays at least exponentially with the number of feedbackbits B,
E[SNR/Capacity loss] ≤ C2− B
2(R−1) .
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems51 / 64
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems52 / 64
A natural generalization
......
...
...
...
...
...
+
+
Transm
itter 1
Transm
itter K
Receiv
er1
Receiv
erL
Relay1
Relay2
RelayR−1
RelayR
How to deal with (wanted or unwanted) interference while preservingcooperative diversity benefits?
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems53 / 64
Beamforming in relay-interferencenetworks
......
...
...
...
...
...
+
+
Transm
itter 1
Transm
itter K
Receiv
er1
Receiv
erL
Relay1
Relay2
RelayR−1
RelayR
K transmitters, R relays in parallel, L receivers.
Each node has a single antenna in half-duplex mode.
Quasi-static channel model.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems54 / 64
CSI knowledge
......
...
...
...
...
...
+
+
Transm
itter 1
Transm
itter K
Receiv
er1
Receiv
erL
s1
sK
v1
vL
Relay1
Relay2
RelayR−1
RelayR
t1 u1
t2 u2
tR−1 uR−1
tRuR
f11f12
f1,R−1
f1R
fK1
fK2
fK,R−1
fKR
g11g21
gR−1,1
gR1
g1L
g2L
gR−1,L
gRL
B feedbackbits
The rth relay knows fir .
Receiver ` knows all fir and gr`.
Each relay and receiver has B bits of partial CSI provided by feedback.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems55 / 64
How to provide the feedback?
......
...
...
...
...
...
+
+
Transm
itter 1
Transm
itter K
Receiv
er1
Receiv
erL
s1
sK
v1
vL
Relay1
Relay2
RelayR−1
RelayR
t1 u1
t2 u2
tR−1 uR−1
tRuR
f11f12
f1,R−1
f1R
fK1
fK2
fK,R−1
fKR
g11g21
gR−1,1
gR1
g1L
g2L
gR−1,L
gRL
B feedbackbits
Two quantization schemes:I Global quantizationI Local quantization
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems56 / 64
Maximal achievable diversityTake - 1
Claim: The maximal achievable diversity in the interference-network isR regardless of the relay operation (AF or DF) or the quality of thefeedback.
The claim is true but incomplete.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems57 / 64
Diversity measures
Generalized Diversity
Suppose that NER(Q) =C
Pd1(logP)d2. Then,
d1 is the first-order diversity.
d2 is the second-order diversity.
The overall diversity is the tuple (d1, d2).
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems58 / 64
Visualizing second-order diversity
Two hypothetical wireless communication schemes:
P (dB)
Pe
Pe =4P 2
Pe =log2 PP 2
5 10 15 20 25 3010−6
10−5
10−4
10−3
10−2
10−1
100
The red scheme with Pe = log2 PP2 has diversity (2,−2).
The blue scheme with Pe = 4P2 has diversity (2, 0).
The error probability with the red scheme “decays much slower”
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems59 / 64
Maximal achievable diversityTake - 2
Claim: The maximal achievable diversity in the interference-network is Rregardless of the relay operation (AF or DF) or the quality of the feedback.
Refined claim:
Diversity Bounds
The maximal diversity in the relay-interference network isI For amplify-and-forward relays:
F (R, 0) if K = 1 (no-interference scenario).F (R,−R) if K > 1 (interference scenario).
I For decode-and-forward relays:F (R, 0) for any K .
Interference results in a second-order diversity loss for AF.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems60 / 64
Main diversity results
Maximum
Diversity
AF DF
K = 1 (R, 0) (R, 0)
K > 1 (R,−R) (R, 0)
Diversity with different quantization strategies
1 Fixed-length Global quantizers achieve the optimal diversity gain withdlog2 Re bits of global feedback per channel state.
2 Fixed-length local quantizers achieve the optimal first-order diversitygain, but they incur a second-order diversity loss of R.
3 Variable-length local quantizers are diversity-optimal. The averagenumber of feedback bits per receiver vanishes as P →∞.
Relay-selection-based quantizers can achieve the optimal diversity gains.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems61 / 64
Main Results
How to deal with (wanted or unwanted) interference while preservingcooperative diversity benefits?
Broadest sense: Network beamforming with distributed quantization.I DF relays achieve full diversity. AF achieves full first-order diversity.I In any case, feedback overhead is extremely low at high power.
Specific relaying method: Choice depends on the system resourcesand the amount of complexity one can tolerate (DF vs AF).
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems62 / 64
Main Results forRelay-Interference Networks
Traditional diversity definitions may not be good enough to comparethe asymptotic reliability of different communication systems.
Despite interference, multi-user relay networks can provide the samediversity as single-user networks.
In terms of diversity, relay selection is an optimal codebook usingquantized feedback information.
Very low-rate CSI quantizers exist that achieve full diversityasymptotically with zero feedback rate.
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems63 / 64
Conclusions
Tremendous challenges need to be addressed to satisfy the demandsof future wireless communication networks.
There is a need for paradigm shifts
Point-to-Point =⇒ Many-to-Many
Competition =⇒ Cooperation
The optimal design of feedback systems is a crucial component ofcurrent and future communication systems
Source coding theory plays an important role in the design offeedback systems
Hamid Jafarkhani (UCI) Distributed Beamforming and Cooperative Communications for Next Generation Wireless Broadband Systems64 / 64